x^y=y
ylnx=lny
y'lnx+y/x=y'/y
dy/dx=y'=(y/x)/(1/y-lnx)=y²/(x-xylnx)
已知由方程x^y=y确定的函数y=f(x)可导,则dy\/dx=
x^y=y ylnx=lny y'lnx+y\/x=y'\/y dy\/dx=y'=(y\/x)\/(1\/y-lnx)=y²\/(x-xylnx)
设函数y=f(x)由方程x+y=e^y确定,求dy\/dx
1+y'=y'e^y 得dy\/dx=y'=1\/(e^y-1)
求参数方程所确定的函数y=f(x)的导数dy\/dx
dy\/dx=(dy\/dt)\/(dx\/dt)=4t=2x
设由方程X-Y=e^(xy) 确定由函数Y=f(x),则dy\/dx=?
1-y'=e^(xy)*(1*y+x*y')y'[xe^(xy)+1]=1-ye^(xy)dy\/dx=y'=[1-ye^(xy)]\/[xe^(xy)+1]
设y=f (x)是由主程y=x^y确定的隐函数,求dy
y=x^y两边对数lny=ylnx 两边求导y'\/y=y'lnx+y\/x 整理得y'=(y^2)\/(1-xylnx)即dy=(y^2)\/(1-xylnx)dx
设y=f(x) 由方程e^y=xy确定,则dy\/dx=? 谢谢
两边对x求导有 y'e^y =y+xy'整理解得 y‘= dy\/dx = x\/(e^y-x)
设y=f(x) 由方程e^y=xy确定,则dy\/dx=?
两边对x求导有 y'e^y =y+xy'整理解得 y‘= dy\/dx = x\/(e^y-x)
y=f(x+y)且f(x)可导 其导数不等于1,则dy\/dx=
dy\/dx=f'(x+y)+f'(x+y)dy\/dx dy\/dx=f'(x+y)\/1-f'(x+y)
设F(x)可导,y=f(x^2),则dy\/dx=?
根据复合函数求导法则 dy\/dx = [f(x^2)]' =f'(x^2) *(x^2)' = 2xf'(x)
